I think the other half of the equation is that his receivers really weren't getting open. Talib was consistently winning the one on one matchup with Demaryius, and Arrington was covering Welker as well as anyone has. The Broncos' passing game excels on the premise that, between the two Thomases and Welker, someone will always be beating single coverage pretty much right off the line. That wasn't true on Sunday night, because Julius wasn't playing, the Pats' defense matches up well on both of their top 2 receivers, the Pats spent a large portion of the night in the dime package, and Eric Decker isn't very good.
If Manning had said to hell with it and started forcing throws into that coverage in those conditions, they Broncos never would have made it to overtime, because they're probably have another 2+ giveaways. You even saw that on their last drive in regulation, where they did score. A handful of plays before, Manning got pressured with no one open and threw up an awful pass that was intercepted by Talib. Only reason the game didn't end right there is because of a defensive holding penalty that had no impact at all on the play.
The Broncos offense did the right thing, philosophically. When they ran the ball they were at least eating up clock and field position, and with the lead that they had that should have been enough. Fortunately for us, Manning was good for one forced throw that got picked, and Montee Ball continues to be Ridley-esque in ball security.